As far as I know, there is no second stage that could reach orbit from a New Shepard, even disregarding the issue of size. It would need to very nearly be a SSTO. The Falcon 9 is well known for staging early, this being part of what makes it feasible to recover its booster, and for ASDS landings its booster is about 150 km downrange and moving at around 2 km/s when it crosses 100 km altitude, where New Shepard reaches a vertical peak at effectively zero velocity.
More realistically, you could use two or more stages. The SS-520-5 rocket is about the right size, you'd increase its 4 kg payload a bit by giving it a boost with a New Shepard (making 4 stages in total). Vacuum-optimized engines could improve things a bit more, but that's roughly the order of magnitude you're looking at.